The partition method for poset-free families
نویسندگان
چکیده
منابع مشابه
The partition method for poset-free families
Given a finite poset P , let La(n, P ) denote the largest size of a family of subsets of an n-set that does not contain P as a (weak) subposet. We employ a combinatorial method, using partitions of the collection of all full chains of subsets of the nset, to give simpler new proofs of the known asymptotic behavior of La(n, P ), as n → ∞, when P is the r-fork Vr, the four-element N poset N , and...
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Given a finite poset P , we consider the largest size La(n, P ) of a family F of subsets of [n] := {1, . . . , n} that contains no subposet P . This continues the study of the asymptotic growth of La(n, P ); it has been conjectured that for all P , π(P ) := limn→∞ La(n, P )/ ( n b 2 c ) exists and equals a certain integer, e(P ). This is known to be true for paths, and for several more general ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2012
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-012-9476-9